The associated production of a single-top with opposite-sign same-flavor (OSSF) di-leptons, \(pp \to t \ell^+ \ell^-\) and \( pp \to t \ell^+ \ell^- + j\) (\(j=\)light jet), can lead to striking tri-lepton \(pp \to \ell^\prime \ell^+ \ell^- + X\) and di-lepton \(pp \to \ell^+ \ell^- + j_b + X\) (\(j_b=b\)-jet) events at the LHC, after the top decays. Although these rather generic multi-lepton signals are flavor-blind, they can be generated by new 4-Fermi flavor changing (FC) \(u_i t \ell \ell\) scalar, vector and tensor interactions (\(u_i \in u,c\)) from different types of FC underlying heavy physics, which we study in this paper. The main backgrounds to these di- and tri-lepton signals arise from \(t \bar t\), \(Z\)+jets and \(VV\) (\(V=W,Z\)) production, but they can be essentially eliminated with a sufficiently high invariant mass selection on the OSSF di-leptons, \(m_{\ell^+ \ell^-}^{\tt min}(OSSF) > 1\) TeV; the use of \(b\)-tagging as an additional selection in the di-lepton final state case also proves very useful. We find, for example, that the expected 95\% CL bounds on the scale of a tensor(vector) \(u t \mu \mu\) interaction, with the current \(\sim 140\) fb\(^{-1}\) of LHC data, are \(\Lambda < 5(3.2) \) TeV or \(\Lambda < 4.1(2.7)\) TeV, if analyzed via the di-muon \(\mu^+ \mu^- + j_b\) signal or the \(e \mu^+ \mu^-\) tri-lepton one, respectively. The expected reach at the HL-LHC with 3000 fb\(^{-1}\) of data is \(\Lambda < 7.1(4.7)\) TeV and \(\Lambda < 2.4(1.5)\) TeV for the corresponding \(u t \mu \mu\) and \(c t \mu \mu\) operators. We also study the potential sensitivity at future 27 TeV and 100 TeV high-energy LHC successors, which, for the \(ut \ell \ell\) operators, can reach \(\Lambda \sim 10-40\) TeV. We furthermore discuss the possible implications of this class of FC 4-Fermi effective interactions on lepton non-universality tests at the LHC.